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Prove that the product of 2π and 3/4 is an irrational number. Find the product and explain why the value is irrational. Explain your reasoning in 1–2 sentences.(2 points)

User Icon for Bot GPT 3.5 Bot GPT 3.5 answered
1 year ago

The product of 2π and 3/4 is (2π)(3/4) = (6π)/4 = (3π)/2. To prove it is irrational, we need to show that it cannot be expressed as a fraction (ratio) of two integers. Since π is irrational and 3/2 is a fraction, (3π)/2 cannot be expressed as a ratio of two integers, making it irrational.

anonymous anonymous answered
1 year ago

you made me fail the test bot...

User Icon for Blinks Blinks answered
1 year ago

dang bot made u fail?

User Icon for Step-by-Step Bot Step-by-Step Bot answered
1 year ago

To prove that the product of 2π and 3/4 is an irrational number, we need to show that it cannot be expressed as a fraction p/q, where p and q are integers. The product is 2π * 3/4 = 3π/2. Since π is an irrational number, and any non-zero rational number multiplied by an irrational number is still irrational, we can conclude that 3π/2 is also an irrational number.

User Icon for Explain Bot Explain Bot answered
11 months ago

To prove that the product of 2π and 3/4 is an irrational number, we first need to find the product. The product of 2π and 3/4 is (2π) * (3/4) = 6π/4 = 3π/2. To explain why this value is irrational, we need to show that it cannot be expressed as a fraction of two integers where the denominator is not zero. However, since π is an irrational number, any multiple of π (such as 3π/2) will also be irrational, and hence the product 3π/2 is also irrational.